Question

Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution.

Answer 1

I would say that the answer is B

Answer 2

Answer:

Option B is correct.

u= x+4

Step-by-step explanation:

Solve the equation:

$(x+4)^2-3(x+4)-3 = 0$

Using substitution:

Let u = x+4

then;

$u^2-3u-3=0$         ....[1]

For a quadratic equation $ax^2+bx+c = 0$ ....[2], then the solution is given by:

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

On comparing equation [1] and [2] we have;

a = 1 , b = -3 and c = -3

then;

$u= \frac{-(-3) \pm \sqrt{(-3)^2-4(1)(-3)}}{2(1)}$

⇒$u= \frac{3 \pm \sqrt{9+12}}{2}$

⇒$u= \frac{3 \pm \sqrt{21}}{2}$

Substitute u = x+4

then;

⇒$x+4= \frac{3 \pm \sqrt{21}}{2}$

Subtract 4 from both sides we have;

$x= \frac{3 \pm \sqrt{21}}{2} - 4= \frac{3 \pm \sqrt{21}-8}{2}$

⇒$x= \frac{3 + \sqrt{21}-8}{2}= \frac{-5 + \sqrt{21}}{2}$

and

$x= \frac{3 - \sqrt{21}-8}{2}$

⇒$x= \frac{-5 - \sqrt{21}}{2}$

Therefore, the solution for the given equation are,

$x= \frac{-5 - \sqrt{21}}{2}$ , $\frac{-5 + \sqrt{21}}{2}$